Extensions of Certain Classical Summation Theorems for the Series 2 ð ¹ 1, 3 ð ¹ 2, and 4 ð ¹ 3 with Applications in Ramanujan's Summations

Yong Sup Kim, Medhat A. Rakha and Arjun K. Rathie

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-26

Abstract:

Motivated by the extension of classical Gauss's summation theorem for the series 2 ð ¹ 1 given in the literature, the authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series 2 ð ¹ 1 , Watson, Dixon and Whipple for the series 3 ð ¹ 2 , and a few other hypergeometric identities for the series 3 ð ¹ 2 and 4 ð ¹ 3 . As applications, certain very interesting summations due to Ramanujan have been generalized. The results derived in this paper are simple, interesting, easily established, and may be useful.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:309503

DOI: 10.1155/2010/309503

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